Subject: Mathematics

Geometry

Master high school Geometry with proofs, transformations, trigonometry, and real-world applications in this self-paced, online course.

Course Type: Standard High School

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Credits: 1.0

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Course Description

Geometry at Excel High School provides a comprehensive exploration of geometric principles, integrating logical reasoning, spatial visualization, and practical applications. Designed for high school students, this self-paced, online course develops critical thinking skills through the study of reasoning and proof, transformations, congruence, triangle relationships, quadrilaterals, similarity, trigonometry, circles, surface area, volume, and probability.

Through ten engaging modules, students learn to construct and analyze geometric proofs, apply transformations, explore triangle congruence and similarity, and use trigonometric ratios to solve both theoretical and real-world problems. Interactive lessons, video tutorials, and digital tools help learners connect geometric concepts to everyday applications, from architecture and engineering to data analysis and design.

The course emphasizes STEM connections, encouraging students to use geometry as a foundation for advanced math and science courses. By the end of the course, learners will be equipped to solve complex geometric problems, model real-world situations, and approach higher-level mathematics with confidence.

Textbook: Geometry Concepts – Excel Education Systems, Inc. ©2019

Course Objectives

Apply geometric concepts and tools to solve problems.

Construct and evaluate geometric proofs using deductive reasoning.

Analyze and perform geometric transformations and demonstrate congruence.

Use trigonometric ratios to solve real-world and theoretical problems.

Model and solve problems involving circles, three-dimensional figures, and probability.

Starting is Easy

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Course Contents

Module TitleModule Topic(s)
The Essentials of Geometry

Spatial reasoning, logical foundations, coordinate geometry

Parallel and Perpendicular Lines

 Line relationships, angle pairs, coordinate methods

Transformations

Rigid motions, dilations, symmetry, real-world modeling

Triangle Congruence

Congruent triangles, proof strategies, structural design

Relationships Within Triangles

Triangle theorems, concurrency, triangle inequalities

Quadrilaterals & Triangle Similarity

Properties of quadrilaterals, similarity in triangles, STEM modeling

Right Triangle Trigonometry

Trigonometric ratios, Pythagorean Theorem, elevation and depression

Properties of Circles

 Angles, arcs, circle equations, geometric design

Surface Area and Volume

Solids, geometric modeling, real-world applications

Probability

Set theory, probability rules, conditional probability, real-world data

Recommended Prerequisites

Carnegie Credits Explained: Our Approach vs. Trimester Credits

Carnegie Credit System
Excel High School follows the Carnegie Credit system, a widely recognized method of measuring student progress based on instructional hours. A single Carnegie credit reflects approximately 120 hours of coursework, typically completed over a full academic year.

Carnegie Credit vs. Trimester Credit
While Carnegie credits are awarded based on total hours over a year, trimester credits divide the school year into three terms. In a trimester system, students complete courses in shorter, intensive sessions, often earning partial credits (e.g., 0.33 or 0.5 per term). In contrast, Excel’s use of Carnegie credits ensures students have ample time to engage deeply with the material and develop a well-rounded understanding at a consistent pace.

Accreditation You Can Trust

Recognized & Respected Nationwide

At Excel High School, we are proud to be regionally accredited by Cognia, along with additional accreditations from NCA, SACS, NWAC, and the Middle States Association. Our programs meet the same rigorous standards as public schools, giving you the confidence of earning a well-respected diploma.

Global Recognition for Our Accredited Diplomas

Excel High School’s regionally accredited diploma is accepted by colleges and universities around the world. With our recognized accreditation, you can confidently pursue higher education wherever your journey takes you.

Accreditation You Can Trust

Recognized & Respected Nationwide

At Excel High School, we are proud to be regionally accredited by Cognia, along with additional accreditations from NCA, SACS, NWAC, and the Middle States Association. Our programs meet the same rigorous standards as public schools, giving you the confidence of earning a well-respected diploma.

Global Recognition for Our Accredited Diplomas

Excel High School’s regionally accredited diploma is accepted by colleges and universities around the world. With our recognized accreditation, you can confidently pursue higher education wherever your journey takes you.